-16t^2+40t+45=0

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Solution for -16t^2+40t+45=0 equation:


Simplifying
-16t2 + 40t + 45 = 0

Reorder the terms:
45 + 40t + -16t2 = 0

Solving
45 + 40t + -16t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-2.8125 + -2.5t + t2 = 0

Move the constant term to the right:

Add '2.8125' to each side of the equation.
-2.8125 + -2.5t + 2.8125 + t2 = 0 + 2.8125

Reorder the terms:
-2.8125 + 2.8125 + -2.5t + t2 = 0 + 2.8125

Combine like terms: -2.8125 + 2.8125 = 0.0000
0.0000 + -2.5t + t2 = 0 + 2.8125
-2.5t + t2 = 0 + 2.8125

Combine like terms: 0 + 2.8125 = 2.8125
-2.5t + t2 = 2.8125

The t term is -2.5t.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5t + 1.5625 + t2 = 2.8125 + 1.5625

Reorder the terms:
1.5625 + -2.5t + t2 = 2.8125 + 1.5625

Combine like terms: 2.8125 + 1.5625 = 4.375
1.5625 + -2.5t + t2 = 4.375

Factor a perfect square on the left side:
(t + -1.25)(t + -1.25) = 4.375

Calculate the square root of the right side: 2.091650066

Break this problem into two subproblems by setting 
(t + -1.25) equal to 2.091650066 and -2.091650066.

Subproblem 1

t + -1.25 = 2.091650066 Simplifying t + -1.25 = 2.091650066 Reorder the terms: -1.25 + t = 2.091650066 Solving -1.25 + t = 2.091650066 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = 2.091650066 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = 2.091650066 + 1.25 t = 2.091650066 + 1.25 Combine like terms: 2.091650066 + 1.25 = 3.341650066 t = 3.341650066 Simplifying t = 3.341650066

Subproblem 2

t + -1.25 = -2.091650066 Simplifying t + -1.25 = -2.091650066 Reorder the terms: -1.25 + t = -2.091650066 Solving -1.25 + t = -2.091650066 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = -2.091650066 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = -2.091650066 + 1.25 t = -2.091650066 + 1.25 Combine like terms: -2.091650066 + 1.25 = -0.841650066 t = -0.841650066 Simplifying t = -0.841650066

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.341650066, -0.841650066}

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